Which areas of applied math are relevant to AI?
EE Math Refresh

AI is an interdisciplinary field.  You can begin by ensuring you are fresh in the mathematics you've already taken. You may already have all the books from your BS and MS.


Infinite series
Logical proofs
Linear algebra and matrices
Analytic geometry, especially the distinction between local and global extremes (minima and maxima), saddle points, and points of inflection
Set theory
Probability, especially Bayes' Theorem and the common probability distributions
Statistics, especially variance and correlation coefficient
Time series
Infinite series
Convergence &mdash; Central to AI batch processing
Partial differentials
Jacobian and Hessian matrices
Multivariate math &mdash; Spaces beyond &#8477;3 are common in AI.
Boundary regions
Discrete math
Criteria for system stability &mdash; Central to real time intelligent control
Bernhard Riemann's manifolds is important for more advanced AI theory


An EE would already understand circuit paths (Gustav Kirchhoff's work, signal transmission, feedback theory, and control theory. To see the connection between AI and EE, Norbert Wiener's seminal work, Cybernetics, 1948, MIT Press, will be a helpful read and give you a clearer picture that both fields have common roots.

Finite Math

Since finite math curricula differ between schools of engineering, this list can be used as a checklist for AI.


Predicate logic and rules engines
Graphs (as in vertices connected by edges) and algorithms for them &mdash; pioneered by Leonhard Euler
Game theory &mdash; John von Neumann and Oskar Morgenstern's Game Theory (published in 1944 but still fresh and pertinent)
Decision trees
Markov chains and the Markov property &mdash; Andrey Markov's work
Information theory &mdash; Claude Shannon's extensions of the thermodynamic concepts of entropy, especially uniqueness, redundancy, relative entropy, and cross entropy &mdash; A necessity to more fully understand feature abstraction and auto-encoding
Chaos theory, especially auto-correlation, for analysis of chaotic system behavior in phase space &mdash; Chaos Theory Tamed, Garnett P. Williams, 1997, provides an excellent overview
Difference between random and pseudo random number generation
Curve fitting and gradient descent, especially the Levenberg–Marquardt algorithm
Stateless versus stateful algorithms, AI system components, and services
Algorithmic theory, especially tail recursion and algorithms for generalization, abstraction, and object recognition
Gödel's uncertainty theorems
Turing completeness and how it does not overturn yet overcomes Gödel's uncertainty
Turing's Imitation Game as a test for conversational intelligence
Other test criteria for intelligence outside the conversation context (i.e. piloting, driving, business intelligence, et cetera)
Topology &mdash; pioneered by Henri Poincaré
Computational linguistics &mdash; pioneered by Richard Hook Richens &mdash; the foundation of much NLP (natural language processing)


Machine Learning

Since machine learning is trending and will probably remain strong even as other AI technologies catch up, there are a few


MLPs (multilayer perceptrons)
Convolution and the use of convolution layers and pooling layers in deep convolution networks
LSTM (long-short term memory) networks, their predecessor RNNs (recurrent neural networks), and some of the newer competitors in the stateful network space
Attention based networks and other gating strategies (largely found online using academic searches for papers)


Soft Sciences

Because most of what is occurring, has occurred, and will occur in AI for the foreseeable future is the replication of human brain capabilities, the EE can point her or his analytical skills at biology (especially neurology), genetics as it may apply to the emergence and control of human intelligence (bioinformatics), psychology (especially cognitive science), and sociology (such as.

Because of the emergence of GANs and other devices that work on the basis of balance and equilibrium, it is useful to recall chemical equilibria and biological stasis.  These concepts apply directly to AI and are likely to play a more major role as the gap between brain network research and computing narrows further.

Automated Vehicles

The obvious emerging AI technology that is nicely aligned with the EE background is the movement of road and air vehicles from human driving and piloting through the various phases of automation.  The goal that most corporations see as the ideal is to progress forward until the driver's seats and cockpits are no longer installed in cars and planes because human interaction other than to provide the transportation destination poses a public safety issue.

Obviously, computer vision, object recognition, sound recognition, and collision avoidance technique are essentials and highly dependent upon rigorous mathematical treatment.